{"id":"https://openalex.org/W2011349622","doi":"https://doi.org/10.1137/s1052623401393128","title":"A Newton Method for Shape-Preserving Spline Interpolation","display_name":"A Newton Method for Shape-Preserving Spline Interpolation","publication_year":2002,"publication_date":"2002-01-01","ids":{"openalex":"https://openalex.org/W2011349622","doi":"https://doi.org/10.1137/s1052623401393128","mag":"2011349622"},"language":"en","primary_location":{"id":"doi:10.1137/s1052623401393128","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1052623401393128","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://ira.lib.polyu.edu.hk/bitstream/10397/4760/1/Dontchev_Newton_method_shape.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5083269925","display_name":"Asen L. Dontchev","orcid":"https://orcid.org/0000-0003-3160-7828"},"institutions":[{"id":"https://openalex.org/I4210159850","display_name":"Annual Reviews","ror":"https://ror.org/05r2g1b90","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I4210159850"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Asen L. Dontchev","raw_affiliation_strings":["Mathematical Reviews"],"affiliations":[{"raw_affiliation_string":"Mathematical Reviews","institution_ids":["https://openalex.org/I4210159850"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112621269","display_name":"Houduo Qi","orcid":"https://orcid.org/0000-0003-3481-4814"},"institutions":[{"id":"https://openalex.org/I31746571","display_name":"UNSW Sydney","ror":"https://ror.org/03r8z3t63","country_code":"AU","type":"education","lineage":["https://openalex.org/I31746571"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Hou-Duo Qi","raw_affiliation_strings":["University Of New south Wales"],"affiliations":[{"raw_affiliation_string":"University Of New south Wales","institution_ids":["https://openalex.org/I31746571"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011886900","display_name":"Liqun Qi","orcid":"https://orcid.org/0000-0002-1112-5250"},"institutions":[{"id":"https://openalex.org/I14243506","display_name":"Hong Kong Polytechnic University","ror":"https://ror.org/0030zas98","country_code":"HK","type":"education","lineage":["https://openalex.org/I14243506"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Liqun Qi","raw_affiliation_strings":["The Hong Kong Polytechnic University"],"affiliations":[{"raw_affiliation_string":"The Hong Kong Polytechnic University","institution_ids":["https://openalex.org/I14243506"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5113599408","display_name":"Hongxia Yin","orcid":null},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"funder","lineage":["https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hongxia Yin","raw_affiliation_strings":["Chinese Academy of Sciences"],"affiliations":[{"raw_affiliation_string":"Chinese Academy of Sciences","institution_ids":["https://openalex.org/I19820366"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5083269925"],"corresponding_institution_ids":["https://openalex.org/I4210159850"],"apc_list":null,"apc_paid":null,"fwci":0.9226,"has_fulltext":true,"cited_by_count":19,"citation_normalized_percentile":{"value":0.73503175,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"13","issue":"2","first_page":"588","last_page":"602"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9776999950408936,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8163279294967651},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.7105939984321594},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.703384518623352},{"id":"https://openalex.org/keywords/newtons-method","display_name":"Newton's method","score":0.6232237219810486},{"id":"https://openalex.org/keywords/inverse-quadratic-interpolation","display_name":"Inverse quadratic interpolation","score":0.6031596064567566},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.5712616443634033},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.540234386920929},{"id":"https://openalex.org/keywords/local-convergence","display_name":"Local convergence","score":0.5221115350723267},{"id":"https://openalex.org/keywords/spline","display_name":"Spline (mechanical)","score":0.4845973253250122},{"id":"https://openalex.org/keywords/spline-interpolation","display_name":"Spline interpolation","score":0.43175989389419556},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4204922318458557},{"id":"https://openalex.org/keywords/quadratic-function","display_name":"Quadratic function","score":0.4178527295589447},{"id":"https://openalex.org/keywords/steffensens-method","display_name":"Steffensen's method","score":0.41149696707725525},{"id":"https://openalex.org/keywords/newtons-method-in-optimization","display_name":"Newton's method in optimization","score":0.38003700971603394},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2811630368232727},{"id":"https://openalex.org/keywords/polynomial-interpolation","display_name":"Polynomial interpolation","score":0.27695992588996887},{"id":"https://openalex.org/keywords/linear-interpolation","display_name":"Linear interpolation","score":0.23300838470458984},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.2283819615840912},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.16553223133087158},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.15527015924453735},{"id":"https://openalex.org/keywords/bilinear-interpolation","display_name":"Bilinear interpolation","score":0.136315256357193},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.08477672934532166},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.05288952589035034},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.05149078369140625}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8163279294967651},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.7105939984321594},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.703384518623352},{"id":"https://openalex.org/C85189116","wikidata":"https://www.wikidata.org/wiki/Q374195","display_name":"Newton's method","level":3,"score":0.6232237219810486},{"id":"https://openalex.org/C143542097","wikidata":"https://www.wikidata.org/wiki/Q3153554","display_name":"Inverse quadratic interpolation","level":5,"score":0.6031596064567566},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.5712616443634033},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.540234386920929},{"id":"https://openalex.org/C117898588","wikidata":"https://www.wikidata.org/wiki/Q6664310","display_name":"Local convergence","level":3,"score":0.5221115350723267},{"id":"https://openalex.org/C10390562","wikidata":"https://www.wikidata.org/wiki/Q581809","display_name":"Spline (mechanical)","level":2,"score":0.4845973253250122},{"id":"https://openalex.org/C31447003","wikidata":"https://www.wikidata.org/wiki/Q545002","display_name":"Spline interpolation","level":3,"score":0.43175989389419556},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4204922318458557},{"id":"https://openalex.org/C166437778","wikidata":"https://www.wikidata.org/wiki/Q50695","display_name":"Quadratic function","level":3,"score":0.4178527295589447},{"id":"https://openalex.org/C173443657","wikidata":"https://www.wikidata.org/wiki/Q7606635","display_name":"Steffensen's method","level":5,"score":0.41149696707725525},{"id":"https://openalex.org/C179127668","wikidata":"https://www.wikidata.org/wiki/Q17086396","display_name":"Newton's method in optimization","level":4,"score":0.38003700971603394},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2811630368232727},{"id":"https://openalex.org/C88080468","wikidata":"https://www.wikidata.org/wiki/Q637347","display_name":"Polynomial interpolation","level":4,"score":0.27695992588996887},{"id":"https://openalex.org/C171836373","wikidata":"https://www.wikidata.org/wiki/Q2266329","display_name":"Linear interpolation","level":3,"score":0.23300838470458984},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.2283819615840912},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.16553223133087158},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.15527015924453735},{"id":"https://openalex.org/C205203396","wikidata":"https://www.wikidata.org/wiki/Q612143","display_name":"Bilinear interpolation","level":2,"score":0.136315256357193},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.08477672934532166},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.05288952589035034},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.05149078369140625},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"score":0.0},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/s1052623401393128","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1052623401393128","pdf_url":null,"source":{"id":"https://openalex.org/S928796702","display_name":"SIAM Journal on Optimization","issn_l":"1052-6234","issn":["1052-6234","1095-7189"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Optimization","raw_type":"journal-article"},{"id":"pmh:oai:ira.lib.polyu.edu.hk:10397/4760","is_oa":true,"landing_page_url":"http://hdl.handle.net/10397/4760","pdf_url":"http://ira.lib.polyu.edu.hk/bitstream/10397/4760/1/Dontchev_Newton_method_shape.pdf","source":{"id":"https://openalex.org/S4306400205","display_name":"PolyU Institutional Research Archive (Hong Kong Polytechnic University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I14243506","host_organization_name":"Hong Kong Polytechnic University","host_organization_lineage":["https://openalex.org/I14243506"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Journal/Magazine Article"},{"id":"pmh:oai:eprints.soton.ac.uk:29640","is_oa":false,"landing_page_url":"https://eprints.soton.ac.uk/29640/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401019","display_name":"ePrints Soton (University of Southampton)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I43439940","host_organization_name":"University of Southampton","host_organization_lineage":["https://openalex.org/I43439940"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":{"id":"pmh:oai:ira.lib.polyu.edu.hk:10397/4760","is_oa":true,"landing_page_url":"http://hdl.handle.net/10397/4760","pdf_url":"http://ira.lib.polyu.edu.hk/bitstream/10397/4760/1/Dontchev_Newton_method_shape.pdf","source":{"id":"https://openalex.org/S4306400205","display_name":"PolyU Institutional Research Archive (Hong Kong Polytechnic University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I14243506","host_organization_name":"Hong Kong Polytechnic University","host_organization_lineage":["https://openalex.org/I14243506"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Journal/Magazine Article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320322598","display_name":"Hong Kong Polytechnic University","ror":"https://ror.org/0030zas98"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2011349622.pdf","grobid_xml":"https://content.openalex.org/works/W2011349622.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W68609084","https://openalex.org/W84287112","https://openalex.org/W1491846897","https://openalex.org/W1545571671","https://openalex.org/W1551360398","https://openalex.org/W1979152443","https://openalex.org/W1992688650","https://openalex.org/W2001508169","https://openalex.org/W2015270939","https://openalex.org/W2024076993","https://openalex.org/W2047668748","https://openalex.org/W2076982017","https://openalex.org/W2079278943","https://openalex.org/W2087236370","https://openalex.org/W2088055586","https://openalex.org/W2731844756","https://openalex.org/W4242272985"],"related_works":["https://openalex.org/W3143080231","https://openalex.org/W1518402494","https://openalex.org/W3001734434","https://openalex.org/W2044725063","https://openalex.org/W2366009225","https://openalex.org/W2808820944","https://openalex.org/W4225141671","https://openalex.org/W2358373416","https://openalex.org/W2381745354","https://openalex.org/W2011349622"],"abstract_inverted_index":{"In":[0,22],"1986,":[1],"Irvine,":[2],"Marin,":[3],"and":[4],"Smith":[5],"proposed":[6],"a":[7,37,44],"Newton-type":[8],"method":[9,32,48],"for":[10],"shape-preserving":[11],"interpolation":[12],"and,":[13],"based":[14],"on":[15],"numerical":[16],"experience,":[17],"conjectured":[18],"its":[19],"quadratic":[20,28,52],"convergence.":[21,53],"this":[23],"paper,":[24],"we":[25],"prove":[26],"local":[27],"convergence":[29],"of":[30,46],"their":[31],"by":[33],"viewing":[34],"it":[35],"as":[36],"semismooth":[38],"Newton":[39],"method.":[40],"We":[41],"also":[42],"present":[43],"modification":[45],"the":[47,57],"which":[49],"has":[50],"global":[51],"Numerical":[54],"examples":[55],"illustrate":[56],"results.":[58]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-03-10T16:38:18.471706","created_date":"2025-10-10T00:00:00"}